This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A340453 #11 Mar 11 2021 11:42:29
%S A340453 1,1,1,1,2,0,1,1,2,1,1,0,2,1,0,2,2,0,1,1,2,1,1,-1,2,1,2,1,2,1,0,1,1,1,
%T A340453 1,0,2,2,1,1,2,-1,1,2,2,1,0,0,3,0,1,1,2,0,1,1,2,2,1,0,2,1,0,1,2,0,1,1,
%U A340453 0,1,2,2,2,1,2,0,2,-1,0,1,2
%N A340453 G.f.: Product_{n>=0} (1 - x^(5*n+5))^2 / ( (1 - x^(5*n+1))*(1 - x^(5*n+4)) ).
%F A340453 G.f.: Sum_{n>=0} x^(1*n)/(1 - x^(5*n+2)) - x^2 * Sum_{n>=0} x^(3*n)/(1 - x^(5*n+4)).
%F A340453 G.f.: Sum_{n>=0} x^(2*n)/(1 - x^(5*n+1)) - x^2 * Sum_{n>=0} x^(4*n)/(1 - x^(5*n+3)).
%F A340453 G.f.: Sum_{n>=0} x^(1*n)/(1 - x^(5*n+2)) - x^2 * Sum_{n>=0} x^(4*n)/(1 - x^(5*n+3)).
%F A340453 G.f.: Sum_{n>=0} x^(2*n)/(1 - x^(5*n+1)) - x^2 * Sum_{n>=0} x^(3*n)/(1 - x^(5*n+4)).
%F A340453 G.f.: [ Sum_{n>=0} x^n/(1 - x^(5*n+1)) - x^3 * Sum_{n>=0} x^(4*n)/(1 - x^(5*n+4)) ] * R(x), where R(q) is the expansion of Ramanujan's continued fraction (A007325).
%e A340453 G.f.: P(q) = 1 + q + q^2 + q^3 + 2*q^4 + q^6 + q^7 + 2*q^8 + q^9 + q^10 + 2*q^12 + q^13 + 2*q^15 + 2*q^16 + q^18 + q^19 + 2*q^20 + ...
%e A340453 Given the g.f. of this sequence,
%e A340453 P(q) = Product_{n>=0} (1 - q^(5*n+5))^2 / ( (1 - q^(5*n+1))*(1 - q^(5*n+4)) ),
%e A340453 and the g.f. of A340454,
%e A340453 Q(q) = Product_{n>=0} (1 - q^(5*n+5))^2 / ( (1 - q^(5*n+2))*(1 - q^(5*n+3)) ),
%e A340453 then R(q) = P(q)/Q(q) where
%e A340453 Q(q) = 1 + q^2 + q^3 + q^4 - q^5 + 2*q^6 + q^8 + q^9 + q^10 + q^12 - q^13 + q^14 + 2*q^15 + q^16 + 2*q^18 - q^19 + q^20 + ...
%e A340453 and
%e A340453 R(q) = 1 + q - q^3 + q^5 + q^6 - q^7 - 2*q^8 + 2*q^10 + 2*q^11 - q^12 - 3*q^13 - q^14 + 3*q^15 + 3*q^16 - 2*q^17 - 5*q^18 - q^19 + 6*q^20 + ...;
%e A340453 here, R(q) is the expansion of Ramanujan's continued fraction (A007325).
%o A340453 (PARI) {a(n) = my(A = prod(m=0,n, (1 - x^(5*m+5))^2 / ( (1 - x^(5*m+1))*(1 - x^(5*m+4)) +x*O(x^n)) )); polcoeff(A,n)}
%o A340453 for(n=0,80,print1(a(n),", "))
%o A340453 (PARI) {a(n) = my(A = sum(m=0,n, x^(1*m)/(1 - x^(5*m+2) +x*O(x^n)) ) - x^2 * sum(m=0,n, x^(3*m)/(1 - x^(5*m+4) +x*O(x^n)) )); polcoeff(A,n)}
%o A340453 for(n=0,80,print1(a(n),", "))
%o A340453 (PARI) {a(n) = my(A = sum(m=0,n, x^(2*m)/(1 - x^(5*m+1) +x*O(x^n)) ) - x^2 * sum(m=0,n, x^(4*m)/(1 - x^(5*m+3) +x*O(x^n)) )); polcoeff(A,n)}
%o A340453 for(n=0,80,print1(a(n),", "))
%Y A340453 Cf. A007325, A340454, A340455, A340456.
%K A340453 sign
%O A340453 0,5
%A A340453 _Paul D. Hanna_, Jan 16 2021